具非线性中立项的广义Emden-Fowler微分方程的振动性  

Oscillation of Generalized Emden-Fowler Differential Equations with Nonlinear Neutral Term

作　　者：张晓建 Zhang Xiaojian(Faculty of Science,Shaoyang University,Hunan Shaoyang 422004)

机构地区：[1]邵阳学院理学院,湖南邵阳422004

出　　处：《数学物理学报（A辑）》2018年第4期728-739,共12页Acta Mathematica Scientia

基　　金：湖南省教育厅科研项目(10C1189);湖南省教育厅教学改革研究项目(2016jg671)~~

摘　　要：研究了一类具有一个非线性中立项的二阶非线性变时滞广义Emden-Fowler型泛函微分方程{a(t)|[x(t)+p(t)x~ɑ(T(t))'|^(β-1)[x(t)+p(t)x~ɑ(T(t))'}'+q(t)f(|x(δ(t))|^(γ-1)x(δ(t)))+0(t≥t_0)的振动性.利用广义的Riccati变换、Bernoulli不等式和Yang不等式,在两种情形∫^(+∞)_(t_(0)) a^(-1/β)(t)dt=+∞和∫^(+∞)_(t_(0)) a^(-1/β)(t)dt<+∞下建立了该类方程振动的若干新的判别准则,这些准则推广且改进了现有文献中的一些结果,所举例子说明这些定理的条件是比较宽松的.We study the oscillatory behavior of a certain class of second-order nonlinear vari-able delay generalized Emden-Fowler functional differential equations with a nonlinear neutralterm of the form{a(t)|[x(t)+p(t)x^a(t))]^t|^β-1[x(t)+p(t)x^a(t(t))t)]}^t+q(t)f(|x(δ(t)))=0(t≥t0)By using the generalized Riccati transformation and Bernoulli's inequality and Yang's inequal-ity,we establish some new oscillation criteria for the equations under the cases when∫^+∞t0a^-1/β(t)dat=+∞,∫^+∞t0a^-1/β(t)dat<+∞the results obtained extend and improve some related results reported in the literature,Exam-ples.are provided to illustrate assumptions in our theorems are less restrictive.

关 键 词：振动性 泛函微分方程 非线性中立项 RICCATI变换 

分 类 号：O175.1[理学—数学]